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An \( \mathrm{X} \) band RADAR used for surveillance transmits a peak power of \( 20 \mathrm{~kW} \) at \( 10 \mathrm{GHz} \). The radar uses a dish antenna with a gain of \( 40 \mathrm{~dB} \). The receiver has a bandwidth of \( 25 \mathrm{MHz} \) and a noise figure of \( 10 \mathrm{~dB} \) operating at room temperature \( (290 \mathrm{~K}) \). The radar is used to detect an airplane with a radar cross section of \( 10 \mathrm{~m}^{2} \) at a distance of \( 1 \mathrm{~km} \). (a) Compute the return signal level \( \operatorname{Pr} \) (in watts)? (b) Determine the SNR (in decibels) at the receiver output?

To calculate the return signal level Pr, we need to use the radar equation: Pr = G * P * ?^2 * ? / (4?R^2) Where: G is the antenna gain (in line